How do you solve the coin change problem using DP?

Given coins and target amount, find minimum coins needed (or number of ways). For minimum coins: dp[i] = min coins for amount i. Initialize dp[0]=0, others=infinity. For each amount i and each coin c, if c<=i: dp[i] = min(dp[i], dp[i-c]+1). For counting ways: dp[i] += dp[i-c]. Time O(amount * coins), space O(amount). The greedy approach doesn't always work (e.g., [1,3,4] making 6).